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380

Kybic and Unser

Figure 9.18: The axial, sagital, and coronal views of the two CT brain volumes (one in red, second one in green) prior to registration. Meaningful comparison is difficult. (Color slide.)

Figure 9.19: The axial, sagital, and coronal views of the two CT brain volumes (one in red, second one in green) after the registration. The volumes are aligned, and the large and medium-scale differences were compensated by the registration. This permits to identify more subtle differences. (Color slide.)

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Questions

1.What is image registration?

2.What is a correspondence function?

3.What is image warping?

4.What are the usual assumptions in motion analysis?

5.How would you use an atlas for segmentation?

6.Which four attributes do the authors use to classify registration algorithms?

7.What is the purpose of interpolation?

8.What is the relation between variational methods minimizing a scalar criterion and methods described using PDEs? [For further study.]

9.Why should a warping model be adapted to the image?

10.What is the purpose of regularization in image registration?

11.What is the essence of multiresolution?

12.Explain the notion of consistency in the image registration context.

13.Try classify a typical landmark registration algorithm according to the framework described in the first part of this chapter.

14.Why does the Laplacian variational criterion not penalize affine deformation?

15.Why are radial basis functions called radial?

16.What is landmark interpolation?

17.Explain the notion of separability for B-spline basis functions and its impact on speed?

18.What is the consequence of setting the virtual spring weights α too high or too low?

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19.How does the registration result depend on the chosen optimization algorithm?

20.What is the relation between the reduction and expansion operators R and E?

21.Does the positivity of the Jacobian guarantee the global invertibility of the deformation?

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Bibliography

[1]Bookstein, F., Morphometric Tools for Landmark Data: Geometry and Biology, Cambridge University Press, Cambridge, 1997.

[2]Mitiche, A. and Bouthemy, P., International Journal of Computer Vision, Vol. 19, pp. 29–55, 1996.

[3]Weese, J. et al., IEEE Transactions on Information Technology in Biomedicine, Vol. 1, pp. 284–293, December 1997.

[4]Asari, K. V., Sanjiv, K., and Radhakrishnan, D., IEEE Transactions on Medical Imaging, Vol. 18, p. 345, April 1999.

[5]Brown, L., ACM Computing Surveys, Vol. 24, p. 326–376, December 1992.

[6]Kybic, J., Thevenaz,´ P., and Unser, M., Multiresolution spline warping for EPI registration, In: Proceedings of SPIE, Vol. 3813, pp. 571–579, SPIE, Denver, Colorado, July 1999.

[7]Bajcsy, R. and Kovaciˇc,ˇ S., Computer Vision, Graphics, and Image Processing, Vol. 46, pp. 1–21, 1989.

[8]Unser, M., Aldroubi, A., and Eden, M., IEEE Transactions on Signal Processing, Vol. 41, No. 2, pp. 821–832, February 1993.

[9]Unser, M., Aldroubi, A., and Eden, M., IEEE Transactions on Signal Processing, Vol. 41, No. 2, pp. 834–848, February 1993.

[10]de Boor, C., A Practical Guide to Splines, Springer-Verlag, New York, 1978.

[11]Meijering, E. H. W., Niessen, W. J., and Viergever, M. A., Quantitative Medical Image Analysis, Vol. 5, No. 2, pp. 111–126, 2001.

[12]Thevenaz,´ P., Blu, T., and Unser, M., IEEE Transactions on Medical Imaging, Vol. 19, No. 7, pp. 739–758, July 2000.

[13]Satter, M. and Goshtasby, A., Registration of deformed images, In: Image Registration Workshop, pp. 221–229, NASA Goddard Space Flight Center, Greenbelt, MD, 1997.

384

Kybic and Unser

[14]Faugeras, O. and Keriven, R., IEEE Transactions on Image Processing, Vol. 7, No. 3, pp. 336–344, March 1998.

[15]Spinei, A., Pellerin, D., and Herault,´ J., Signal Processing, Vol. 65,

pp.347–362, 1998.

[16]Bernard, C., Fast optical flow computation with discrete wavelets, Technical report, Ecole Polytechnique, Paris, 1997.

[17]Suhling,¨ M., Arigovindan, M., Jansen, C., Hunziker, P., and Unser, M., Myocardial motion analysis and visualization from echocardiograms, In: Progress in Biomedical Optics and Imaging, Vol. 4, No. 23 Sonka, M. and Fitzpatrick, J., eds., Vol. 5032 of Proceedings of the SPIE International Symposium on Medical Imaging: Image Processing (MI’03),

pp.306–313, San Diego CA, USA, February 17-20, 2003, part I.

[18]Wu, Y., Kanade, T., Cohn, J., and Li, C., Image registration using waveletbased motion model, In: Proceedings of Image Registration Workshop, Le Moigne, J., ed. 1997.

[19]Rohr, K., Stiehl, H. S., Sprengel, R., Beil, W., Buzug, T. M., Weese, J., and Kuhn, M. H., Point-based elastic registration of medical image data using approximating thin-plate splines, In: Visualization in Biomedical Computing, Hohne,¨ K. H. and Kikinis, R., eds., pp. 297–306, SpringerVerlag, Berlin 1996.

[20]McGregor, B., Pattern Recognition, Vol. 31, No. 6, pp. 805–817, 1998.

[21]Bookstein, F. L., IEEE Transactions Pattern Anal. Mach. Intell., Vol. 6, No. 6, pp. 567–585, June 1989.

[22]Davatzikos, C., Prince, J., and Bryan, R., IEEE Transactions on Medical Imaging, Vol. 15, No. 1, February 1996.

[23]Huang, C., Chang, W., Wu, L., and Wang, J., IEEE Transactions on Medical Imaging, Vol. 16, No. 5, October 1997.

[24]Rosch,¨ P. et al., Robust 3D deformation field estimation by template propagation, In: Proceedings of MICCAI, pp. 521–530, 2000.

[25]Yeung, F., Levinson, F., Fu, D., and Parker, K. J., IEEE Transactions on Medical Imaging, Vol. 17, No. 6, pp. 945–956, December 1998.

Elastic Registration for Biomedical Applications

385

[26]Horn, B. and Schunck, B., Artificial Inteligence, Vol. 17, pp. 185–203, 1981.

[27]Christensen, G., Deformable Shape Models for Anatomy, Ph.D. Dissertation, Washington University, Saint Louis, Mississippi, 1994.

[28]Christensen, G., Joshi, S., and Miller, M., IEEE Trans. on Med. Imaging, Vol. 16, No. 6, pp. 864–877, December 1997.

[29]Bro-Nielsen, M. and Gramkow, C., Fast fluid registration of medical images, In: Visualization in Biomedical Computing, Hohne,¨ K. H. and Kikinis, R., eds., pp. 267–276, Springer-Verlag, Berlin 1996.

[30]Iosifescu, D. V. et al., Neuroimage, Vol. 14, No. 6, pp. 14–25, 1997.

[31]Tai, Y., Lin, K., Hoh, C., Huang, S., and Hoffman, E., IEEE Transactions on Nuclear Science, Vol. 44, No. 4, August 1997.

[32]Hermosillo, G., Variational Methods for Multimodal Image Matching, Ph.D. Dissertation, INRIA, Available at ftp://ftp-sop.inria.fr /robotvis/html/Papers/hermosillo:02.ps.gz, 2002,

[33]Schormann, T., Henn, S., and Zilles, K., A new approach to fast elastic alignment with applications to human brains, In: Visualization in Biomedical Computing, Hohne,¨ K. H. and Kikinis, R., eds., SpringerVerlag, Berlin 1996.

[34]Kjems, U., Strother, S. C., Anderson, J., Law, I., and Hansen, L. K., Enhancing the multivariate signal of 15 O water PET studies with a new nonlinear neuroanatomical registration algorithm, IEEE Transactions on Medical Imaging, Vol. 18, No. 4, pp. 306–319, April 1999.

[35]Bergen, J., Anandan, P., Hanna, K., and Hingorani, R., Hierarchical model-based motion estimation, In: Second European Conference on Computer Vision (ECCV’92), pp. 237–252, Springer-Verlag, Berlin 1992.

[36]Thevenaz,´ P., Ruttimann, U. E., and Unser, M., IEEE Transactions on Image Processing, Vol. 7, No. 1, pp. 1–15, January 1998.

[37]Sicotte, N., Woods, R., and Mazziotta, J., Neuroimage, Vol. 3, No. 3, June 1996, II International Conference on Functional Mapping of the Human Brain.

386

Kybic and Unser

[38]Kiebel, S., Ashburner, J., Poline, J., and Friston, K., Neuroimage, No. 5, 1997.

[39]Ashburner, J. and Friston, K. J., Nonlinear spatial normalization using basis functions, In: Brain Warping, Toga, A. W., ed., pp. 254–266, Academic Press, San Diego, 1999.

[40]Szeliski, R. and Coughlan, J., International Journal of Computer Vision, Vol. 22, pp. 199–218, 1997.

[41]Szeliski, R. and Shum, H.-Y., IEEE Trans. Pattern Anal. Mach. Intell., Vol. 18, No. 12, pp. 1199–1207, December 1996.

[42]Lester, H. and Arridge, S., Summarising fluid registration by thinplate spline warps with many landmarks, In: Medical Image Understanding and Analysis, July 1997, Available at http://www.robots. ox.ac.uk/˜mvl/miua97/.

[43]Zhang, Z., International Journal of Computer Vision, Vol. 13, No. 2,

pp.119–152, December 1994.

[44]Weese, J., Rosch,¨ P., Netsch, T., Blaffert, T., and M., Q., Gray-value based registration of CT and MR images by maximization of local correlation, In: Proceedings of MICCAI, 1999.

[45]Thevenaz,´ P. and Unser, M., IEEE Transactions on Image Processing, Vol. 9, No. 12, pp. 2083–2099, December 2000.

[46]Kim, B., Boes, J., Frey, K., and Meyer, C., Mutual information for automated multimodal image warping, In: Visualization in Biomedical Computing, Hohne,¨ K. H. and Kikinis, R., ed., Springer-Verlag, 1996.

[47]Maes, F., Collignong, A., Vandermeulen, D., Marchal, G., and Suetens, P., IEEE Transactions on Medical Imaging, Vol. 16, No. 2, pp. 187–198, April 1997.

[48]Studholme, C., Hill, D., and Hawkes, D., Automated Three-dimensional Medical Physics, Vol. 24, No. 1, January 1997.

[49]Nikou, C., Heitz, F., and Armspach, J.-P., Pattern Recognition, No. 32,

pp.1351–1368, 1999.

Elastic Registration for Biomedical Applications

387

[50]Duchon, J., Splines minimizing rotation-invariant semi-norms in Sobolev spaces, In: Constructive Theory of Functions of Several Variables, Schempp, W. and Zeller, K., eds., pp. 85–100, Springer-Verlag, Berlin, 1977.

[51]Suter, D. and Chen, F., IEEE Transactions on Medical Imaging, Vol. 19, No. 4, pp. 295–305, April 2000.

[52]Hermosillo, G., Chefd’hotel, C., and Faugeras, O., ijcv, Vol. 50, No. 3,

pp.329–343, November 2002.

[53]Davis, C. Q. and Freeman, D. M., Optical Engineering, Vol. 4, No. 37,

pp.1290–1298, April 1998.

[54]Fleet, D. and Jepson, A., International Journal of Computer Vision, Vol. 5, No. 1, pp. 77–104, 1990.

[55]Horn, B. and Weldon, E., The International Journal of Computer Vision, Vol. 2, No. 1, pp. 51–76, June 1988.

[56]Tomasi, C. and Manduchi, R., IEEE Trans. Pattern Anal. Mach. Intell., Vol. 20, No. 3, March 1998.

[57]Unser, M., Pelle, G., Brun, P., and Eden, M., Computer analysis of M- mode echocardiograms: estimation of spatial deformation with time, In: Cardiovascular Dynamics and Models, pp. 304–310, Institut National de la Sante´ et de la Recherche Medicale,´ Paris, 1988.

[58]Gimel’farb, G., Pattern Recognition Letters, Vol. 23, No. 4, pp. 431–442, 2002.

[59]Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., Numerical Recipes in C, Cambridge University Press, 2nd edn., 1992.

[60]Strang, G. and Fix, G., An Analysis of the Finite Element Method, Wellesley-Cambridge Press, 1988.

[61]Martin, J., Pentland, A., Sclaroff, S., and Kikinis, R., IEEE Trans. Pattern Anal. Mach. Intell., Vol. 2, No. 2, February 1998.

[62]Moulin, P., Krishnamurthy, R., and Woods, J., IEEE Transactions on Image Processing, Vol. 6, No. 12, pp. 1606–1620, December 1997.

388

Kybic and Unser

[63]Brandt, A., Math. Comput., Vol. 31, No. 138, pp. 339–390, 1977.

[64]Yoshida, H., Removal of normal anatomic structures in radiographs using wavelet-based non-linear variational method for image matching, In: Wavelet Applications in Signal and Imaging Processing VI, Vol. 3458, pp. 174–181, SPIE, 1998.

[65]Amit, Y., SIAM Journal on Scientific Computing, Vol. 15, No. 1, pp. 207– 224, 1994.

[66]Dennis, Jr. J., and Schnabel, R., Numerical Methods for Unconstrained Optimisation and Nonlinear Equations, SIAM J. Math. Anal., 1997.

[67]Thirion, J., Fast non-rigid matching of 3D medical images, Technical Report 2547, INRIA, Nice, May 1995.

[68]Heitz, F., Perez, P., and Bouthemy, P., Comput. Vis. Graph. Image Process., Vol. 59, No. 1, pp. 125–134, 1994.

[69]Miller, M., Joshi, S., and Christensen, G., Large deformation fluid diffeomorphisms for landmark and image matching, In: Brain Warping, Toga, A., ed., pp. 115–132, Academic Press, San Diego, 1999.

[70]Christensen, G. and Johnson, H., IEEE Transactions on Medical Imaging, Vol. 20, No. 7, pp. 568–582, July 2001.

[71]Musse, O., Heitz, F., and Armspach, J.-P., IEEE Transactions on Medical Imaging, Vol. 10, No. 7, pp. 1081–1093, July 2001.

[72]Zitova,´ B. and Flusser, J., Image and Vision Computing, No. 21, pp. 977– 1000, 2003.

[73]Warfield, S., Robatino, A., Dengler, J., Jolesz, F., and Kikinis, R., Nonlinear registration and template-driven segmentation, In: Brain Warping, Toga, A. W., ed., pp. 67–84, Academic Press, San Diego, 1999.

[74]Gee, J., Pattern Recognition, No. 32, pp. 99–111, 1999.

[75]van den Elsen, P. A., Pol, E.-J. D., and Viergever, M. A., IEEE Engineering in Medicine and Biology, pp. 26–39, March 1993.

[76]Lester, H. and Arridge, S. R., Pattern Recognition, Vol. 32, No. 1, pp. 129– 149, January 1999.

Elastic Registration for Biomedical Applications

389

[77]Verard, L., Allain, P., Travere, J., Baron, J. C., and Bloyet, D., IEEE Transactions on Medical Imaging, Vol. 16, No. 5, pp. 6100–616, October 1997.

[78]Lam, N. S.-N., The American Cartographer, Vol. 10, No. 2, pp. 129–149, 1983.

[79]Franke, R., Mathematics of Computation, Vol. 38, No. 157, pp. 181–200, 1982.

[80]Unser, M. and Blu, T., Wavelets and radial basis functions: A unifying perspective, In: Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing VIII, Vol. 4119, pp. 487–493, San Diego, CA, 2000.

[81]Werntges, H. W., Partitions of unity improve neural function approximators, In: Proceedings of IEEE International Conference on Neural Networks, Vol. 2, pp. 914–918, San Francisco, CA, 1993.

[82]Mallat, S., A Wavelet Tour of Signal Processing, Academic Press, San Diego, CA, 1998.

[83]Gabrani, M. and Tretiak, O. J., Pattern Recognition, No. 32, pp. 87–97, 1999.

[84]Duchon, J., Revue Franc¸ aise d’Automatique, Informatique et Recherche Operationelle, Vol. 10, No. 12, pp. 5–12, December 1976.

[85]Kybic, J., Blu, T., and Unser, M., IEEE Transactions on Signal Processing, Vol. 50, No. 8, pp. 1965–1976, August 2002, ftp://cmp.felk.cvut.cz/ pub/cmp/articles/kybic/Kybic-ieeeSP2002a.pdf.

[86]Kybic, J., Blu, T., and Unser, M., IEEE Transactions on Signal Processing, Vol. 50, No. 8, pp. 1977–1985, August 2002, ftp://cmp.felk.cvut.cz/ pub/cmp/articles/kybic/Kybic-ieeeSP2002b.pdf.

[87]Powell, M. J. D., The Theory of radial basis function approximation in 1990, In: Advances in Numerical Analysis II: Wavelets, Subdivision Algorithms and Radial Functions, Light, W. A., ed., pp. 105–210, Oxford University Press, Oxford, UK, 1992.

[88]Kybic, J., Biomedical Image Processing by Elastic Warping, Ph.D. Dissertation, Ecole Polytechnique Fed´erale´ de Lausanne, Lausanne,